The author’s investigations in the class T of typically real functions f(z) in the disk |z| < 1 are continued. The region of values of f′(z 1) in the class of functions f ∈ T with fixed values f(z 1) and f(r j ) (j = 1, 2) is determined. Here, |z 1| < 1, Im z 1 ≠ 0, 0 < r j < 1 (j = 1, 2). Bibliography: 4 titles.
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E. G. Goluzina, “The region of values of the systems {f(z 1), f′(z 1)} and {f(z 1), f(z 2)} in the class of typically real functions,” Zap. Nauchn. Semin. POMI, 254, 65–75 (1998).
E. G. Goluzina, “The region of values of the systems {f(z 1), f(z 2), f′(z 2)} and {f(z 1), f′(z 1), f″(z 1)} in the class of typically real functions,” Zap. Nauchn. Semin. POMI, 286, 48–61 (2002).
E. G. Goluzina, “A distortion theorem for the class of typically real functions,” Zap. Nauchn. Semin. POMI, 357, 33–45 (2008).
E. G. Goluzina, “The region of values of the systems {f(z 1), f(z 2), f(z 3)} in the class of typically real functions,” Zap. Nauchn. Semin. POMI, 302, 5–17 (2003).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 371, 2009, pp. 171–175.
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Goluzina, E.G. To distortion theorems for typically real functions. J Math Sci 166, 222–224 (2010). https://doi.org/10.1007/s10958-010-9863-7
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DOI: https://doi.org/10.1007/s10958-010-9863-7